Your floor joist is sitting atop your wall, which is supporting the weight of your floor above. Adding the supports shown in blue will not provide much support to the joist where you cut it. You risk having some serious sag in the floor above, or structural failure at worst.
Unfortunately, I don't think there is much you can do in this instance.
schribes7762 t1_ixzlql5 wrote
Reply to Removing part of a floor joist to embed a projector. by mejelic
No.
Your floor joist is sitting atop your wall, which is supporting the weight of your floor above. Adding the supports shown in blue will not provide much support to the joist where you cut it. You risk having some serious sag in the floor above, or structural failure at worst.
Unfortunately, I don't think there is much you can do in this instance.